Question

How do you graph and find the discontinuities of `1 /(x+6)`?

Answer 1

graph{1/(x+6) [-10, 10, -5, 5]} and `x=-6`

Explanation:

Essentially it's transforming the graph `y=1/x` into `y=1/(x+6)` by translating `x` `6` units in the negative `x`-direction. Discontinuities occur when the function is undefined, i.e. `x=-6`, at which the graph is undefined. You can show this by drawing the vertical like `x=6` and showing that this line never intersects the graph of `y=1/(x+6)`